Uhlenbeck-Ford model

Functional form

The Uhlenbeck-Ford model is given by :

U_{UF}(r)=-{\frac {p}{\beta }}\ln \left(1-e^{-(r/\sigma )^{2}}\right)

where

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p > 0 } is a scaling factor;
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta \equiv (k_B T)^{-1} } is the well depth (energy);
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r \equiv |\mathbf{r}_1 - \mathbf{r}_2|} is the interparticle distance;
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is a length-scale parameter.